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Question

Find the respective terms for the following $$APs$$
$$a_{2}=38,a_{6}=-22$$ find $$a_{1},a_3.a_4,a_5$$


Solution

$$a_{2}=38$$   $$a_{6}=-22$$
$$a_2=a+d=38$$  ...........(1)
$$a_6=a+5d=-22$$ .......(2)
Equation (1)-(2), gives
$$-4d=60$$
$$\Rightarrow d=15$$
Sunstitutue $$d=15$$ in Equation (1)
$$a+(-15)=38$$
$$\Rightarrow a=53$$
$$\therefore a_3=a+2d=53+2(-15)=23$$
$$\therefore a_4=a+3d=53+3(-15)=8$$
$$\therefore a_5=a+4d=53+4(-15)=-7$$
$$\therefore\,a_1=53, a_3=23,a_4=8,a_5=-7$$

Mathematics

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